Quantum ring solitons and nonlocal effects in plasma wake field excitations

Year: 2012

Authors: Fedele R., Tanjia F., De Nicola S., Jovanovic D., Shukla P.K.

Autors Affiliation: Dipartimento di Scienze Fisiche, Università di Napoli “Federico II,” and INFN, Napoli, Italy;
Istituto Nazionale di Ottica – C. N. R.,Pozzuoli (NA), Italy;
Institute of Physics, University of Belgrade, Belgrade, Serbia;
Center of Advanced Studies in Physical Sciences, Ruhr-Universitat Bochum, Bochum, Germany

Abstract: A theoretical investigation of the quantum transverse beam motion for a cold relativistic charged particle beam travelling in a cold, collisionless, strongly magnetized plasma is carried out. This is done by taking into account both the individual quantum nature of the beam particles (single-particle uncertainty relations and spin) and the self consistent interaction generated by the plasma wake field excitation. By adopting a fluid model of a strongly magnetized plasma, the analysis is carried out in the overdense regime (dilute beams) and in the long beam limit. It is shown that the quantum description of the collective transverse beam dynamics is provided by a pair of coupled nonlinear governing equations. It comprises a Poisson-like equation for the plasma wake potential (driven by the beam density) and a 2D spinorial Schrodinger equation for the wave function, whose squared modulus is proportional to the beam density, that is obtained in the Hartree’s mean field approximation, after disregarding the exchange interactions. The analysis of this pair of equations, which in general exhibits a strong nonlocal character, is carried out analytically as well as numerically in both the linear and the nonlinear regimes, showing the existence of the quantum beam vortices in the form of Laguerre-Gauss modes and ring envelope solitons, respectively. In particular, when the relation between the plasma wake field response and the beam probability density is strictly local, the pair of the governing equations is reduced to the 2D Gross-Pitaevskii equation that allows one to establish the conditions for the self focusing and collapse. These conditions include the quantum nature of the beam particles. Finally, when the relation between the plasma wake field response and the beam probability density is moderately nonlocal, the above pair of equations permits to follow the spatio-temporal evolution of a quantum ring envelope soliton. Such a structure exhibits small or violent breathing, but it remains very stable for long time.

Journal/Review: PHYSICS OF PLASMAS

Volume: 19 (10)      Pages from: 102106-1  to: 102106-15

More Information: This work was supported partially by INFN Sezione di Napoli, Italy, within the NTA project COMB and partially by the Grant No. 171006 of the Serbian Ministry of Science and Education. One of the authors (D.J.) acknowledges the financial support from the Fondo Affari Internazionali of INFN and the kind hospitality of Dipartimento di Scienze Fisiche, Universita di Napoli Federico II. The work of P. K. S. was supported by the DFG.
KeyWords: Thermal-wave Model; Particle-beam Transport; Electron-beam; Storage; Instabilities; Acceleration; Vortex
DOI: 10.1063/1.4757214

Citations: 15
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